On characterizations of solution sets of interval-valued quasiconvex programming problems

In this article, we study several characterizations of solution sets of LU-quasiconvex interval-valued function. Firstly, we provide Gordan’s theorem of the alternative of interval-valued linear system. As a consequence of this theorem, we find the normalized gradient of the interval-valued function is constant over the solution set when its gradient is not zero. Further, we discuss Lagrange multiplier characterizations of solution sets of LU-quasiconvex interval-valued function and provide optimality conditions of interval-valued optimization problem under the generalized Mangasarian-Fromovitz constraint qualifications. We provide illustrative examples in the support of our theory.